title: Assessing sample entropy of physiological signals by the norm component matrix algorithm: application on muscular signals during isometric contraction.
abstract: Sample Entropy (SampEn) is a popular method for assessing the unpredictability of biological signals. Its calculation requires to preliminarily set the tolerance threshold r and the embedding dimension m. Even if most studies select m=2 and r=0.2 times the signal standard deviation, this choice is somewhat arbitrary. Effects of different r and m values on SampEn have been rarely assessed, because of the high computational burden of this task. Recently, however, a fast algorithm for estimating correlation sums (Norm Component Matrix, NCM) has been proposed that allows calculating SampEn quickly over wide ranges of r and m. The aim of our work is to describe the structure of SampEn of physiological signals with different complex dynamics as a function of m and r and in relation to the correlation sum. In particular, we investigate whether the criterion of "maximum entropy" for selecting r previously proposed for Approximate Entropy, also applies to SampEn; and whether information from correlation sums provides indications for the choice of r and m. For this aim we applied the NCM algorithm on electromyographic and mechanomyographic signals during isometric muscle contraction, estimating SampEn over wide ranges of r (0.01 ≤ r ≤ 5) and m (from 1 to 11). Results indicate that the "maximum entropy" criterion to select r in Approximate Entropy cannot be applied to SampEn. However, the analysis of correlation sums alternatively suggests to choose r that at any m maximizes the number of "escaping vectors", i.e., data points effectively contributing to the SampEn estimation.
authors.forename: Paolo
authors.initials: P
authors.lastname: Castiglioni
authors.forename: Sebastian
authors.initials: S
authors.lastname: Żurek
authors.forename: Jaroslaw
authors.initials: J
authors.lastname: Piskorski
authors.forename: Marcin
authors.initials: M
authors.lastname: Kośmider
authors.forename: Przemyslaw
authors.initials: P
authors.lastname: Guzik
authors.forename: Emiliano
authors.initials: E
authors.lastname: Cè
authors.forename: Susanna
authors.initials: S
authors.lastname: Rampichini
authors.forename: Giampiero
authors.initials: G
authors.lastname: Merati
mesh_terms: D000465:Algorithms; D004576:Electromyography; D019277:Entropy; D006801:Humans; D007537:Isometric Contraction / Q000502:physiology*; D008297:Male; D009132:Muscles / Q000502:physiology*